Bremen 2017 – wissenschaftliches Programm
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P: Fachverband Plasmaphysik
P 15: Helmholtz Graduate School II
P 15.18: Poster
Dienstag, 14. März 2017, 16:30–18:30, HS Foyer
Radial basis functions for the Vlasov equation — •Anna Yurova1,2, Katharina Kormann1,2, and Caroline Lasser2 — 1Max-Planck-Institut für Plasmaphysik — 2Technische Universität München
Solving the full kinetic equations can help in understanding possible shortcomings of gyrokinetics. We consider a reformulation of the classical semi-Lagrangian method using a representation of the distribution function in a radial basis.
Using Radial Basis Functions (RBF) discretization for the Vlasov equation allows for more flexibility in the choice of the computational domain and can have spectral accuracy. We choose Gaussians which allow for exact integration and resemble the structure of the solution in velocity space. Therefore, it is possible to simulate an unbounded domain in velocity instead of cutting it as it is currently done in existing mesh-based methods.
We investigate the inherent ill-conditionioning of the linear system arising from the RBF-discretization. This ill-conditioning is linked to the width of the Gaussian function. We study different choices of the width of our radial basis in order to establish the optimal setup for our problem.